Biomedical Engineering Reference
In-Depth Information
flux,
j
F
, can bewritten as
D
=
μ
k
T
Z
Ca
(4.13)
j
F
=−
∇
D
C
(4.14)
where
Z
Ca
(
=
2), is the charge of calcium ion and
C
is its
concentration gradient,
∇
C
=
ρ
+
∂
z
z
.
D
is estimated to be 8.0
×
10
−
10
m
2
s
−
1
, while for
C
=
1Mm
−
1
,
j
F
is estimated to be 8.0
×
10
−
10
Mm
−
1
s
−
1
. Where ionic concentration equals its gradient,
fluxduetoFick'sdiffusion,
j
F
,isgreaterthanthe
X
-directedfluxdue
to E field mobility,
j
E
, for E fields below 2.58
×
10
−
2
Vm
−
1
(Plonsey
and Barr, 1988).
Our two estimates notwithstanding, the ability of sharks and
sting-rays to sense ultra-weak E fields as small as 0.5
×
10
−
6
V
m
−
1
is experimentally undisputed (Kalmijn, 1981). Given that such
ambient E field levels will produce accumulated offsets well below
the thermal effect over the estimated averaging time and volume,
then the only sensible conclusion is that such creatures must have
an innate ability to magnify the ambient E fields. Fishman suggests
summation of the output of the large numbers of cell receptors in
the ampullae (Fig. 4.19) (1987).
Another method by which magnification of ambient E fields
could be achieved is in the geometric shape of the fins themselves.
Such fins have very slender profiles, and the edges separating
the upper and lower parts of these fins create a sharp media
discontinuity. Depending on the 'thinness ratio' near the edge
of the fins, a concept discussed in Chapter 4 with regard to
metallic implants (in antenna theory, the 'thinness ratio' is the ratio
between height and wire radius), incident E fields are enhanced at
locations directly adjacent to the body surface, near the ampullae
pores. Chen et al. (1986) used a moment method employing 424
surface patches to calculate the surface fields and body currents
of a realistically shaped human phantom model exposed to ELF
fields. They calculated enhancement factors of 50 at the tips of
the outstretched fingers (forming a crucifix posture), akin to the
outstretchedpredatorialelasmobranchfish.Thedifferencebetween
∂
∂ρ
